Question

simplify the expression \\(\frac{y^6}{y^7}\\). write your answer using only positive exponents. the solution is \\(\frac{\square}{\square}\\).

Explanation:

Step1: Apply exponent rule for division

When dividing exponents with the same base, we subtract the exponents: $a^m \div a^n = a^{m - n}$. So for $\frac{y^6}{y^7}$, we have $y^{6 - 7}$.

Step2: Simplify the exponent

Calculate $6 - 7 = -1$, so we get $y^{-1}$.

Step3: Convert to positive exponent

Using the rule $a^{-n} = \frac{1}{a^n}$, $y^{-1}$ becomes $\frac{1}{y^1}$ or $\frac{1}{y}$.

Answer:

$\frac{1}{y}$